Death of period-doublings: Locating the homoclinic-doubling cascade

DOI10.1016/S0167-2789(00)00133-0zbMath1011.34036OpenAlexW2038781735MaRDI QIDQ5940284

Alan R. Champneys, Bart E. Oldeman, Bernd Krauskopf

Publication date: 1 June 2003

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(00)00133-0

zbMATH Keywords

homoclinic-doubling cascadeFeigenbaum constantsaddle-type equilibriumvector fields

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (13)

Codimension-3 bifurcations of a class of homoclinic loop with saddle-point ⋮ BIFURCATIONS OF HOMOCLINIC ORBIT CONNECTING TWO NONLEADING EIGENDIRECTIONS ⋮ Parametrically forced stably stratified cavity flow: complicated nonlinear dynamics near the onset of instability ⋮ A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock–Paper–Scissors ⋮ Homoclinic organization in the Hindmarsh–Rose model: A three parameter study ⋮ NONORIENTABLE MANIFOLDS IN THREE-DIMENSIONAL VECTOR FIELDS ⋮ HOMOCLINIC BRANCH SWITCHING: A NUMERICAL IMPLEMENTATION OF LIN'S METHOD ⋮ Multiparameter critical situations, universality and scaling in two-dimensional period-doubling maps ⋮ Traveling waves in the Baer and Rinzel model of spine studded dendritic tissue ⋮ Global bifurcations to strange attractors in a model for skew varicose instability in thermal convection ⋮ Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with D4 symmetry ⋮ A strange attractor in the unfolding of an orbit-flip homoclinic orbit ⋮ BIFURCATION, BURSTING AND SPIKE GENERATION IN A NEURAL MODEL

Uses Software

• AUTO
• HomCont

Cites Work

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